Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Harmonic maps into sub-Riemannian Lie groups
View through CrossRef
<abstract><p>We define harmonic maps between sub-Riemannian manifolds by generalizing known definitions for Riemannian manifolds. We establish conditions for when a horizontal map into a Lie group with a left-invariant metric structure is a harmonic map. We show that sub-Riemannian harmonic maps can be abnormal or normal, just as sub-Riemannian geodesics. We illustrate our study by presenting the equations for harmonic maps into the Heisenberg group.</p></abstract>
American Institute of Mathematical Sciences (AIMS)
Title: Harmonic maps into sub-Riemannian Lie groups
Description:
<abstract><p>We define harmonic maps between sub-Riemannian manifolds by generalizing known definitions for Riemannian manifolds.
We establish conditions for when a horizontal map into a Lie group with a left-invariant metric structure is a harmonic map.
We show that sub-Riemannian harmonic maps can be abnormal or normal, just as sub-Riemannian geodesics.
We illustrate our study by presenting the equations for harmonic maps into the Heisenberg group.
</p></abstract>.
Related Results
Pointwise semi-slant Riemannian maps into almost Hermitian manifolds and Casorati inequalities
Pointwise semi-slant Riemannian maps into almost Hermitian manifolds and Casorati inequalities
UDC 514
As a natural generalization of slant submanifolds [B.-Y. Chen, Bull. Austral. Math. Soc., 41, No. 1, 135 (1990)], slant submersions [B. Şahin, Bull. Math. Soc. Sci. Math....
Conformal Hemi-Slant Riemannian Maps
Conformal Hemi-Slant Riemannian Maps
In this study, we define conformal hemi-slant Riemannian maps from an almost Hermitian manifold to a Riemannian manifold as a generalization of conformal anti-invariant Riemannian ...
Locally Isometric Riemannian Analytic Spaces
Locally Isometric Riemannian Analytic Spaces
Classes of locally isometric Riemannian analytic manifolds are studied. A generalization of the concept of completeness is given. We consider the Lie algebra ???? of all Killing ve...
Analisa Perbandingan GPS Google Maps Dan GPS Google Earth Dalam Penentuan Titik Koordinat Breeding Place
Analisa Perbandingan GPS Google Maps Dan GPS Google Earth Dalam Penentuan Titik Koordinat Breeding Place
INTISARINyamuk Aedes Aegypti menularkan penyakit DBD (Demam Berdarah Dengue) ke manusia dengan gigitannya. Breeding Place merupakan berkembangbiaknya jentik nyamuk di tempat pe...
EXTERIOR DIFFERENTIAL FORMS ON RIEMANNIAN SYMMETRIC SPACES
EXTERIOR DIFFERENTIAL FORMS ON RIEMANNIAN SYMMETRIC SPACES
In the present paper we give a rough classification of exterior differential forms on a Riemannian manifold. We define conformal Killing, closed conformal Killing, coclosed conform...
Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Given a (quasi-)twilled pre-Lie algebra, we first construct a differential graded Lie algebra ([Formula: see text]-algebra). Then we study the twisting theory of (quasi-)twilled pr...
Deformations and abelian extensions of compatible pre-Lie superalgebras
Deformations and abelian extensions of compatible pre-Lie superalgebras
In this paper, we give cohomologies and deformations theory, as well as abelian extensions for compatible pre-Lie superalgebras. Explicitly, we first introduce the notation of a co...
Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable. Th...